What is the Greatest Common Factor of 33999 and 34008?

Greatest common factor (GCF) of 33999 and 34008 is 3.

GCF(33999,34008) = 3

We will now calculate the prime factors of 33999 and 34008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33999 and 34008.

How to find the GCF of 33999 and 34008?

We will first find the prime factorization of 33999 and 34008. After we will calculate the factors of 33999 and 34008 and find the biggest common factor number .

Step-1: Prime Factorization of 33999

Prime factors of 33999 are 3, 7, 1619. Prime factorization of 33999 in exponential form is:

33999 = 3¹ × 7¹ × 1619¹

Step-2: Prime Factorization of 34008

Prime factors of 34008 are 2, 3, 13, 109. Prime factorization of 34008 in exponential form is:

34008 = 2³ × 3¹ × 13¹ × 109¹

Step-3: Factors of 33999

List of positive integer factors of 33999 that divides 33999 without a remainder.

1, 3, 7, 21, 1619, 4857, 11333

Step-4: Factors of 34008

List of positive integer factors of 34008 that divides 33999 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 109, 156, 218, 312, 327, 436, 654, 872, 1308, 1417, 2616, 2834, 4251, 5668, 8502, 11336, 17004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33999 and 34008. The biggest common factor number is the GCF number.
So the greatest common factor 33999 and 34008 is 3.

Also check out the Least Common Multiple of 33999 and 34008